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Abstract:
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We fit a proportional hazards model (PH) to interval-censored survival data by subdividing each subject's failure interval into sub-intervals (SI). Using all interval endpoints in the dataset, those that fall into the subject's interval are then used as the cut-points for the SI. Each SI has a weight calculated from a parametric Weibull model. The sum of the weights for each subject equals 1. A weighted PH model is then fit with multiple observations per subject, where the upper end of each SI is used as the observed failure time with the associated weight. A baseline Weibull distribution is chosen as it is the only survival distribution in both the accelerated failure time and PH families. We iterate between estimating the baseline Weibull distribution and fitting the weighted PH model until the parameter estimates converge. The regression parameter estimates are fixed as an offset when we update the estimates of the Weibull distribution. Simulation results demonstrate apparently unbiased parameter estimation for the correctly specified Weibull model and little to no bias for a misspecified log-logistic model. Breast cosmetic deterioration data (Finkelstein, 1986) are analyzed.
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